Full text of "An analytical and experimental investigation of rotating, non-capillary heat pipes : annual report"

See other formats

XR&BWGAl REPORT SECTIOS
ttSVKL POST' 3CHC

MONTKRKT, CAH;CI.>UA 039'

NPS - 59MX70061A

United States
Naval Postgraduate School

AN ANALYTICAL AND EXPERIMENTAL

INVESTIGATION OF ROTATING, NON-CAPILLARY

HEAT PIPES

ANNUAL REPORT

P. J. MARTO
T. J. DALEY
L. J. BALLBACK

30 JUNE 1970

This document has been approved for public
release and sale; its distribution is unlimited,

FEDDOCS

D 208.14/2:

NPS-59MX70061A

NAVAL POSTGRADUATE SCHOOL
Monterey, California

Rear Admiral R. W. McNitt, USN R. F. Rinehart

Superintendent Academic Dean

ABSTRACT

An analytical review of the operation of rotating, non-capillary
heat pipes is presented, including a discussion of film condensation
on the inside of a rotating, truncated cone. Predicted results so
far obtained indicate that the heat transfer capability of rotating,
non-capillary heat pipes depends upon condenser performance and is
substantially higher than the capability of conventional, wick-
limited heat pipes.

The design and manufacture of an experimental rotating heat
pipe apparatus is also described.

This task was supported by:

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
Defense Purchase Request W - 13,007

TABLE OF CONTENTS

Page

1. INTRODUCTION 1

1.1 Conventional Heat Pipe 1

1.2 The Rotating, Non-Capillary Heat Pipe 2

1.3 Objective 3

2. STATUS OF ANALYTICAL PROGRAM 4

2.1 Limits of Operation 4

2.2 Film Condensation Theory 5

3. STATUS OF EXPERIMENTAL PROGRAM 14
3.1 Description of Equipment 14

4. SUMMARY OF WORK PERFORMED 21

4.1 Analytical Program 21

4.2 Experimental Program 22

5. PROPOSED ACTIVITIES 23

5.1 Analytical Program 23

5.2 Experimental Program 23

BIBLIOGRAPHY 24

INITIAL DISTRIBUTION LIST 40

FORM DD 1473 45

1 . INTRODUCTION

1.1 CONVENTIONAL HEAT PIPE

A heat pipe is a self-contained device which can transport
large quantities of heat at nearly isothermal conditions. Conven-
tionally, it consists of three main parts: a container, a working
fluid, and a capillary wicking structure which is saturated with
the working fluid.

When heat is added to one end of the container, some of the
working fluid evaporates. The resulting vapor flows to the opposite
end of the container, transporting heat as latent heat of vaporiza-
tion. Here the vapor condenses on the cooler surface and releases
the heat to be removed from the structure. The condensate is pumped
back to the evaporator section by capillary action within the wick-
ing structure, thus completing the cycle. The heat pipe is unique
in that it operates with no moving parts, maintains nearly isothermal
conditions, and removes the dependency on gravity through the use
of capillary pumping.

Limits on the heat transfer capabilities of conventional heat
pipes are imposed by a number of fluid -dynamic mechanisms,
including a wick resistance limit, a sonic vapor velocity
limit, a vapor velocity entrainment limit, and also
a wick boiling limit [1,2,3,].* In each case, the heat transfer

♦Numbers in brackets indicate references listed in the Bibliography.

limit is defined to occur when the wick begins to dry out in the
evaporator, causing excessive operating temperatures there. These
limits have been considered in a number of studies [4,5,6] with the
conclusion that, in general, a conventional heat pipe using an or-
dinary working fluid is limited by the rate that the condensate can
be returned to the evaporator due to wick resistance. Under certain
circumstances, nucleate boiling in the wick structure may also limit
operation.

1.2 THE ROTATING, NON-CAPILLARY HEAT PIPE

The wick-resistance and boiling limitations of conventional
heat pipes can be overcome by removing the wick and by utilizing
centrifugal acceleration to return the condensate to the evaporator [7]

The rotating, non-capillary heat pipe is shown schematically in
FIGURE 1. It consists of a sealed, hollow shaft, having a slight
internal taper from one end to the other, and containing a fixed
amount of working fluid. When the shaft is rotated at high speed
about its longitudinal axis, the working fluid collects as an annul us
at the large end. Heat added to this end of the shaft (evaporator)
evaporates the working fluid, generating vapor which then flows
axial ly toward the other end. Heat removed from this end of the
shaft (condenser) condenses the vapor. The centrifugal forces accel-
erate the liquid condensate back to the evaporator to complete the
cycl e .

By removing the wick structure, its limitations on heat transfer
capability are also removed. The rotating, non-capillary heat pipe
can therefore operate at much higher heat fluxes than conventional
heat pipes and has many potential applications [7].

1.3 OBJECTIVE

The overall objective of this research program is to analytically
study the operation of rotating, non-capillary heat pipes and to
experimentally test the performance of these devices.

This annual report describes the work performed through 30 June
1970 under NASA Defense Purchase Request W-13,007 for the Lewis
Research Center, Cleveland, Ohio.

2. STATUS OF ANALYTICAL PROGRAM

2.1 LIMITS OF OPERATION

In a preliminary analysis of the operation of a rotating, non-
capillary heat pipe, Ballback [ 8 ] studied the limitations of var-
ious fluid-dynamic mechanisms which may be imposed on the rotating
pipe. Using existing theoretical equations and experimental corre-
lations, he estimated the limitations imposed by (a) the critical
nucleate boiling heat flux ("burnout"), (b) the entrainment of the
condensate ("flooding"), and (c) the sonic vapor velocity. In
addition, he estimated a condensing limitation by performing a
simplified Mussel t film condensation analysis. He modeled the
condenser section of the heat pipe as a rotating, truncated cone
which had no external thermal resistance. His approximate analyt-
ical expression is applicable to ordinary fluids and can be used
to study the influence of rotational speed, condenser internal
geometry and fluid properties upon rotating heat pipe performance.

Ballback compared his four proposed limitations for a
14.0-inch long rotating heat pipe with a minimum inside diameter
of 2.0-inches and a half-cone angle of 1 degree. His estimated
results are re-plotted in FIGURE 2 for a 1/8-inch thick stainless
steel heat pipe operating with water at 2700 RPM. From these
results, two conclusions were drawn. First of all, the rotating,
non-capillary heat pipe will transfer significantly more heat than

a conventional heat pipe. Secondly, even with the associated un-
certainties in each of the four above-mentioned limitations, the
rotating, non-capillary heat pipe will be condensation limited.
Thus, its performance will be controlled by the amount of heat
that can be removed from the condenser section.

It was therefore concluded that it would be important to more
thoroughly study and understand the condensation mechanism within
rotating, non-capillary heat pipes in an effort (a) to reliably
predict their behavior, and (b) to improve upon their performance.

2.2 FILM CONDENSATION THEORY

In analyzing the condensation mechanism within the rotating
heat pipe, it was assumed that film condensation and not dropwise
condensation occurs. Thus, the working fluid was assumed to
completely wet the inside surface of the condenser and spread out
into a thin condensate film.

The film condensation mechanism within the rotating heat pipe
is complicated by the dynamical flow interactions between the
liquid and the vapor during rotation. Such effects as swirl of
the condensate, interfacial shear between the condensate and the
vapor, axial pressure drop of the vapor, and formation of waves or
ripples in the condensate may be important. It was reasoned that
inclusion of these mechanisms into an initial analytical program
would serve to complicate the analysis without improving upon the
understanding of rotating heat pipe operation. On the other hand,

a fundamental laminar film condensation analysis (similar to
Nusselt's classical analysis [ 9 ])would establish an analytical
reference solution which would be applicable to ordinary fluids.
This solution could be verified experimentally and could be
modified during the latter portion of this research project to
include the above-mentioned mechanisms. In so doing, the relative
importance of each of these mechanisms could be evaluated indiv-
idually, leading perhaps to important design changes and to im-
proved heat pipe performance.

Prior to this investigation, there was no complete solution
for laminar film condensation on the inside of a rotating, trun-
cated cone. In searching the literature, however, it was dis-
covered that in 1961, Sparrow and Hartnett [ 10 ] carried out a
solution for laminar film condensation on the outside of a
rotating cone. They used a boundary layer approach and pointed
out that their similarity solution applies only to cones that are
not too slender. They obtained a condensate film thickness which
remains uniform along the condenser surface, but which depends on
liquid Prandtl Number, Pr, and on the parameter ^ (T -T )/h- .
For ordinary fluids with Prandtl Numbers near unity, and for

C (T -T )/h- <0.1, they found that the film thickness could be
p s w fg

predicted by:

~cpCTs-TJ

6 = I.I07

Pr hf9

cj sm0

( l )

In the above equation,

C = specific heat of the condensate

T ■ saturation temperature of the vapor
T = condenser wall surface temperature
hf = latent heat of vaporization
v ■ kinematic viscosity of the condensate
u = angular velocity of the condenser, and
0 = one half the internal cone angle (half-cone angle).
Their similarity solution was applied during this project to
the inside of a rotating, truncated cone with a geometry defined
in FIGURE 3. This analysis led to the same expression for the
film thickness as predicted by eq'n. (1). When the thermal resis-
tance across the condensate film was included with the condenser
wall resistance and the outside cooling thermal resistance, a
simple expression for the overall heat removal rate from the con-
denser (which in steady state must be the heat transport rate of
the heat pipe) was derived:

ZV! LC(T5 -T,,) ( Ra + ^ sin 0 ) (2)

Qt = i. + t. + I

Equation (2) is valid for thin condensate films and condenser
walls.

where

T a outside ambient fluid temperature

h = outside heat transfer coefficient (which depends on
the exterior cooling mechanism)

t s condenser wall thickness

k = thermal conductivity of the condenser wall

k.* = thermal conductivity of the condensate

and where R , L and 0 are defined in FIGURE 3. Note that in eq'n

(1) the inside wall surface temperature T is not generally known,

but depends on Qt and 6 from the heat transfer rate across the

condensate film:

- ^^M***4- kCsm<*>(Ts-Tw) (3)

Equations (1), (2) and (3) were solved simultaneously for water

condensing on the inside of a stainless steel condenser surface

for which

R„ = 0.730 inches
o

L ■ 9.0 inches
c

t ■ 0.0625 inches, and
0 ■ 1 , 2 and 3 degrees .
The outside heat transfer coefficient was assumed to be
h ■ 500 BTU/hr ft2 °F and h = -. The results at atmospheric pressure
for various rotational speeds are plotted as dashed curves in
FIGURES 4, 5 and 6. Note that the heat removal rate, Qt increases

with rotational speed and half -cone angle, 0. Note also that Q.
depends strongly on the selection of the outside heat transfer
coefficient, h.

This similarity solution, as pointed out earlier, pertains
only to large cone angles and must therefore be approximate for
small half-cone angles 0=1,2 and 3 degrees. In addition, it
leads to a condensate velocity distribution given by

2 9

ucx,y) = ^tfL (sy - i)(Ro4-X3in0) sm0 (4)

where

pr = density of the condensate, and

yf s dynamic viscosity of the condensate.

This velocity does not satisfy the boundary condition that along the

2
condenser end wall at x = 0(y>0), the velocity must be zero.

In an effort to overcome these restrictions, Ball back per-
formed a Nusselt-type analysis for film condensation on the inside
of a rotating, truncated cone [8]. Using the coordinate system
shown in FIGURE 3 and following the classical assumptions used by
Nusselt, he found that the condensate velocity could be expressed by
2 2

U<M) = ^(5y-|)(Ro+^s,n0-5c°s^)(sm0-cos^5|)(5)

Strictly speaking, because of the heat pipe geometry and coordinate
system chosen in FIGURE 3, the condensate velocity is very small
but not exactly zero at x s 0, y>0.

Equation (5) reduces to eq'n (4) if the condensate film is very
thin (i.e., 6 cos 0 « RQ + x sin 0) and if the slope of the con-
densate film, g- is much less than tan 0. The first of these
assumptions will be true under most circumstances. However, the
second assumption will only be satisfied for cones which are not
too slender.

Ballback made both of these assumptions in his analysis in
order to analytically solve for the film thickness. He used the
boundary condition, however, that 6 must be zero at x = 0 to
satisfy the initial condition on the velocity, and arrived at
the following solution for the film thickness

S(X) = 1.107

tpOk-Tj

Prh„

/wsm0 \ v'Ro-»-xsin0>

(6)

This equation differs from eq'n (1) because of its explicit
dependence on x, and predicts an average film thickness which
is less than that predicted by Sparrow and Hartnett [10].

Daley [11] modified Ball back's work to include the thermal
resistances in the condenser wall and in the outside surface cooling
mechanism. Daley numerically integrated for the heat removal rate
Q. using the same boundary condition as Ballback, that at x s 0,
6=0. His results are plotted as the solid curves in FIGURES 4,
5 and 6 for the same heat pipe geometry and operating conditions

as the Sparrow and Hartnett results. Notice that Daley's results
are substantially higher than those predicted by the Sparrow and
Hartnett similarity solution. This is due presumably to the thinner
film thickness which results in Daley's analysis from the boundary
condition that at x ■ 0, 6 = 0. Since both results, however, are
limited to large half-cone angles, the curves shown in FIGURES 4,
5 and 6 remain approximate for cones represented by 0 - 1, 2 and
3 degrees.

The restriction of large half-cone angles was later removed
by Daley [11]. Using the condensate velocity profile given by
eq'n (5) and keeping in all the terms, he arrived at a second-
order, non-linear differential equation for the film thickness:

i-j — iM(sm0-cos0~) (^CRo+xsm0>-^6 cos^)

3 _ 4. A f%

+ (Ro-*-xs(n0-Scos0X^(Ro+xsm^)-^6 cos0)(-^Acos#)

(7)

£ + i. + J-
11

where the right-hand side of this expression is just the rate of

dQt
change of the heat transport rate, g— - . Equation (7) is valid for

all half-cone angles, and reduces upon simplification to existing

theoretical expressions for both a rotating disc [12] at 0 = 90°

and for a rotating cylinder [13] at 0 s 0°.

Daley numerically integrated this expression using a Runge-

Kutta-Gill numerical integration scheme with an IBM 360 Mod 67

digital computer. To start the integration, the following initial

values were selected at x = 0:

6 = «1 (8a) , and

<J* = tan (9 (8b)

From eq'n (5), -j- must be equal to tan 0 at x = 0(y>0) in order
to satisfy the initial condition for the condensate velocity. How-
ever, the initial value of the film thickness 6. is unknown and is

believed to depend on the minimum film thickness 6 . which occurs

at or very near the exit of the condenser. Thus, as stated by
Leppert and Nimmo [13] for condensation on finite surfaces normal to
inertial forces, the starting film thickness at x * 0 is determined

by the minimum film thickness 6 . . They postulate that the
minimum thickness depends on the particular overfall condition
which occurs at the surface's edge. This dependence is shown
schematically in FIGURE 7. Daley used a free overfall condition
(as derived in open channel flow) to approximate the flow over the

corner at the condenser exit. He arrived at a minimum condensate
thickness given by:

S
mm

0.7 m+

(ztr£<o)z(R04- Lcsm<*)3

(9)

where m- is the mass flow rate of the condensate at the exit of

the condenser. He therefore assumed an initial value for 6. and

integrated his equations out to x = L . Using his integrated film

thickness, he solved for m, at x = L and used this result in eq'n

(9) to get «. . He then compared 5m. to his film thickness at
1 ' =» mm r mm

x - L . If the two thicknesses agreed to within .0004 inches, a
solution was obtained. If the two thicknesses did not agree, a new
starting value of 6. was assumed and the integration scheme repeated.

Daley applied this technique to a rotating cylinder with a half-
cone ang*e 0=0°. His results for R = 0.730 inches, L = 9.0 inches
and t ■ 0.0625 inches are plotted in FIGURE 8 for two values of the
outside heat transfer coefficient, h = 500 BTU/hr ft2 °F and h = <•.
Note that this chosen rotating heat pipe 1s attractive even without
an internal taper. For example, at an RPM of 2400, with an out-
side heat transfer coefficient of 500 BTU/hr ft2 °F, this rotating
heat pipe can still transfer about 3 KW of power. Results for half-
cone angles greater than zero have not yet been obtained.

3. STATUS OF EXPERIMENTAL PROGRAM

In order to test rotating, non-capillary heat pipe performance,
an experimental apparatus was designed, manufactured, and partially
assembled.

In designing the equipment, the evaporator section was modeled
after the rotating boiler apparatus which has been used at the Lewis
Research Center for the study of boiling heat transfer coefficients
at high gravity levels [14,15]. The condenser geometry was chosen
to conform to the geometry used in the Analytical Program (See
FIG. 3). In addition to safety and flexibility, a strong influence
in the overall design was the desire to visually observe the mechan-
isms that will occur within the heat pipe during operation.

3.1 DESCRIPTION OF EQUIPMENT

The main components of the rotating, non-capillary heat pipe
are grouped into the evaporator, condenser, auxiliary equipment, and
instrumentation. FIGURE 9 is a schematic diagram of the test
apparatus. A cross-sectional drawing of the assembled heat pipe
is pictured in FIGURE 10, and FIGURE 11 is a photograph of the
machined pieces of the rotating heat pipe prior to assembly.
Evaporator

The evaporator is a 3.125-inch inside diameter stainless steel
cylinder, 5. 90- inches long. One end is flanged to an outside dia-
meter of 5.906-inches to accommodate the condenser and to support

a large, single row precision ball bearing. The other end is
flanged to an outside diameter of 4.50-inches to accommodate two
pyrex glass end windows. The inner window presses against a teflon-
coated metallic o-ring and is separated from the outer window by a
compressed fiber gasket. Both windows are held in place by a
stainless steel end cap. (See FIG. 10.)

The evaporator is helically wound with an 11 -gage Chromel-A
heater wire in a 3/16-inch outside diameter Inconel sheath. The
heater coils are silver soldered in place. They are coated with a
thin layer of Sauereisen cement and are packed with asbestos insula-
tion to reduce radial heat losses. In addition, a 1/16-inch wide
radial groove is machined into the evaporator wall on either end of
the heater element to reduce axial heat losses. Electrical power
to the heater is passed by a graphite brush assembly through bronze
collector rings. The power supply is a DC motor-generator capable
of delivering 150 amperes at 250 volts.

A photograph of the machined evaporator section is shown in
FIGURE 12.
Condenser

The condenser is a 10.0-inch long stainless steel, truncated
cone with a 3 degree half-cone angle and with a 1/16-inch wall thick-
ness. The large end of the condenser is flanged to bolt to the evap-
orator and has an inside diameter of 2.50-inches. The small end is
machined into a cylinder 1.46-inches inside diameter, by 1.50-inches

long. It is flanged to accommodate a cylindrical end plug. Each
flanged joint is sealed with a teflon-coated, metallic o-ring.

The stainless steel condenser end plug is hollowed out to
allow the pressure transducer arm to be passed through its inside
face, and to allow the drive shaft to be threaded and keyed in
place. The outer end of the plug is machined down to four flat
sides, each 7/8-inch wide and 7/8-inch long to accommodate phenolic
thermocouple junction boards.

A photograph showing the condenser and end plug prior to
assembly may be seen in FIGURE 13.
Auxiliary Equipment

The auxiliary equipment are grouped into the drive assembly,
test stand, spray cooling assembly and safety shields.
Drive Assembly. The drive assembly consists of the drive shaft,
support bearing, pulley and variable drive motor. The drive shaft
is a 3/4-inch diameter stainless steel cylinder which is hollowed
out to allow the instrumentation leads to be connected to the slip-
ring unit. The outside diameter of the shaft is stepped in several
places to thread into the condenser end plug, to accommodate a 2.65-
inch diameter drive pulley, and to support a double row, angular
contact bearing. Each end of the shaft is internally threaded. The
pressure transducer arm is screwed into one end and the slip- ring
coupling into the other. The shaft is screwed securely into the
condenser end plug and is keyed in place. Torque is applied to

the shaft by a V-belt using a 2 HP, 3 phase variable speed motor.
The motor is capable of speeds from 450 to 4500 RPM and is equipped
with a magnetic disc brake and an electric remote control unit.
Test Stand. The test stand was designed so that the rotating heat
pipe could be rigidly supported and tested with its longitudinal
axis oriented from 0 to 90 degrees from the horizontal. Both the
heat pipe assembly and the variable drive motor are bolted into
steel support plates which are welded to a 4-inch diameter iron
pipe. This support pipe is held in place by three 2-inch thick
steel clamps which are supported 2 feet off the ground by a 1/4-inch
steel welded structure. The support pipe (with the heat pipe assem-
bly and drive motor rigidly attached as a unit) can be turned to any
orientation and clamped securely in place prior to heat pipe opera-
tion. FIGURE 14 shows a photograph of the heat pipe assembly and
variable drive motor mounted on the test stand.
Spray Cooling Assembly. The rotating heat pipe condenser is cooled
by spraying a fine mist of tap water onto its outside surface during
rotation. The spray cooling assembly is two stationary, 13-inch
diameter, stainless steel half -cylinders with welded ends. These
two half -cylinders completely enclose the condenser section of the
heat pipe. The bottom half -cylinder is bolted to the steel support
plate on which the heat pipe is mounted. The top half -cylinder 1s
bolted to the bottom half after the heat pipe is in place and ready
for operation. When mounted, each end of the half -cylinders fits

within 1/8-inch deep grooves machined into the condenser end flanges,
and is sealed with a felt gasket.

Each half -cylinder contains four spray nozzles which are mounted
at the same axial position but at different circumferential positions.
Using various nozzles, droplet sizes ranging from 300 to 600 microns
can be obtained. The cooling water is fed from copper lines to a
stainless steel mixing tube soldered onto the top half -cylinder.
The coolant flows from the mixing tube through plastic tubing to
each of the spray nozzles. It drains through the bottom half -cylinder
and is collected by a second mixing tube before being dumped to the
building drain lines.

Safety Shields. To ensure safe operation, the entire heat pipe is
surrounded by 1/8-inch thick stainless steel shielding which easily
bolts to the steel support plate.
Instrumentation

Eight copper-constantan thermocouples were selected to be
used on the rotating heat pipe. These thermocouples are 1/16-inch
in diameter, Inconel sheathed, and magnesium oxide insulated, and
were calibrated at 212°F, 500°F and 700°F by the Thermoelectric
Company. Four of the thermocouples will be placed within 1/16-inch
diameter drilled wells at different radial positions within the
evaporator wall to monitor the radial heat transfer into the
evaporator. One thermocouple will be suspended in the liquid
annulus of the evaporator to measure the bulk liquid temperature.

Another thermocouple will be suspended in the vapor space at the
evaporator exit to measure the saturation temperature of the vapor.
Two additional thermocouples will be soldered into the wall of the
condenser at different axial positions to monitor the heat transfer
through the condenser. The leads from these thermocouples will be
brought along the sides of the condenser and through the small rear
condenser flange to the phenolic junction boards on the condenser
end plug. From the junction boards, the leads will go inside the
shaft to the slip-ring unit. The temperature of the spray coolant
will be measured in the inlet and exit condenser mixing tubes using
two quartz thermometers.

The saturation pressure of the vapor will be measured by a
1/4-inch diameter semi-conductor pressure transducer mounted in the
vapor space. The transducer is temperature compensated and will be
threaded on a 1/4-inch diameter transducer arm that extends from
the drive shaft through the end plug and into the vapor space. The
transducer leads will pass along the transducer arm, out through the
shaft to the junction boards, and back into the shaft to the slip-
rings. The pressure of the spray coolant will be indicated by a
pressure tap on the coolant feed line. The spray coolant flow rate
will be measured with a rotameter prior to spraying.

The rotational speed of the heat pipe will be found using both
a Hewlett-Packard optical tachometer with a frequency counter and an
electronic strobe light.

The electrical power into the evaporator will be measured using
a calibrated voltmeter, ammeter combination. The power level will
be controlled by a field rheostat placed in parallel with the DC
motor-generator.

All the rotating instrumentation leads will be attached to a
22 terminal mercury slip-ring unit which is rated at less than 10
microvolts noise at speeds to 4000 RPM. The slip-ring output will
be fed to a Hewlett-Packard 2010 C Data Acquisition System which
has an accuracy of ± 0.5 microvolts.

4. SUMMARY OF WORK PERFORMED

4.1 ANALYTICAL PROGRAM

A preliminary analysis was performed on the operation of the
rotating, non-capillary heat pipe. Nusselt's film condensation
theory was extended to include centrifugal accelerations on the
inside of a rotating, truncated cone. An approximate condensation
limit was derived for ordinary fluids and compared to the boiling,
entrainment and sonic limits for water using a given heat pipe
geometry. The results indicate the rotating heat pipe to be con-
densation limited.

Approximate film condensation heat transfer results from the
Nusselt-type analysis were substantially higher than those obtained
from the modified similarity solution of Sparrow and Hartnett [10]
for half-cone angles 0=1,2 and 3 degrees. An improved numerical
solution was established which is valid for all half-cone angles,
and which Includes the thermal resistances in the condenser wall
and in the outside cooling mechanism. This solution depends upon
knowledge of the condensate film thickness at the exit of the con-
denser. Results have been obtained for a rotating cylinder with
no internal taper (I.e., 0 s 0°) and show a strong dependence of
the heat removal rate on the outside heat transfer coefficient.
Results have not yet been obtained for half -cone angles greater than
zero.

4.2 EXPERIMENTAL PROGRAM

The design and manufacture of a safe, flexible heat pipe
apparatus was completed. A stainless steel, rotating, non-capillary
heat pipe was designed so that the condenser geometry, the test
fluid or the condenser outside cooling method can be varied. It
was also designed for operation in any orientation with respect to
gravity.

The evaporator is a 5. 90- inch long cylinder with a 3.125-inch
inside diameter. The condenser is a 10.0-inch long truncated cone
with an internal half-cone angle of 3 degrees. The heat pipe is
capable of rotational speeds to 4000 RPM, and contains a 30 KW
DC-heater and a pyrex glass end window.

It is instrumented with eight copper-constantan thermocouples
and a semi-conductor pressure transducer which will be monitored
with a 22-terminal mercury slip-ring unit and a data acquisition
system.

5. PROPOSED ACTIVITIES

5.1 ANALYTICAL PROGRAM

1. The improved Nusselt film condensation analysis, using a
free overfall boundary condition at the condenser exit,
will be extended to other condenser cone geometries.

2. The importance of the condensate film thickness at the
condenser exit, and the importance of the free overfall
boundary condition upon the condenser heat transfer rate,
will be further studied.

3. An attempt will be made to investigate the effects of
liquid-vapor interfacial shear, and condensate surface
waves or ripples upon rotating heat pipe operation.

5.2 EXPERIMENTAL PROGRAM

1. The assembly of all the heat pipe components will be
completed.

2. The heat pipe will be tested in a horizontal orientation
at different rotational speeds using water, alcohol and
f reon .

3. Similar tests will be made with a different condenser
half -cone angle.

4. It may become necessary to repeat several water heat pipe
tests using different condenser exit designs to experimentally
investigate what influence the condensate overfall condition
may have on heat pipe operation.

BIBLIOGRAPHY

1. Cotter, T. P., "Theory of Heat Pipes", Los Alamos Scientific
Laboratory Report, LA-3246-MS, February, 1965.

2. Marcus, B. D., "On the Operation of Heat Pipes", TRW Space
Technology Laboratories Report, May, 1965.

3. Los Alamos Scientific Laboratory Quarterly Status Report,
LA-4109-MS, February, 1969.

4. Carnesale, A., Cosgrove, J. H. and Ferrell, J. K. , "Operating
Limits of the Heat Pipe", AEC/SANDIA Heat Pipe Conference,
Vol. 1, October, 1966.

5. Busse, C. A., "Heat Pipe Thermionic Converter Research in
Europe", Paper presented at the 4th Intersociety Energy Con-
version Engineering Conference, Washington, D.C., September, 1969,

6. Marto, P. J. and Mosteller, W. L., "Effect of Nucleate Boiling
on the Operation of Low Temperature Heat Pipes", ASME Paper
No. 69-HT-24, presented at the ASME-AIChE 11th National Heat
Transfer Conference, Minneapolis, Minnesota, August, 1969.

7. Gray, V. H., "The Rotating Heat Pipe - A Wickless Hollow Shaft
for Transferring High Heat Fluxes", ASME Paper No. 69-HT-19,
presented at the ASME-AIChE 11th National Heat Transfer Con-
ference, Minneapolis, Minnesota, August, 1969.

8. Ballback, L. J., "The Operation of a Rotating, Wickless Heat
Pipe", M.S. Thesis, Naval Postgraduate School, Monterey,
California, December, 1969.

9. Nusselt, W., "Die Oberflachenkondensation des Wasserdampfes",
Z. Ver. Deutsch. Ing., 60, pp. 541-569, 1916.

10. Sparrow, E. M. and Hartnett, J. P, "Condensation on a Rotating
Cone", Journal of Heat Transfer, 83, pp 101-102, February, 1961.

11. Daley, T. J., "The Experimental Design and Operation of a
Rotating, Wickless Heat Pipe", M. S. Thesis, Naval Postgraduate
School, Monterey, California, June, 1970.

12. Sparrow, E. M. and Gregg, J. L., "A Theory of Rotating Condensa-
tion", Journal of Heat Transfer, 81_, pp. 113-120, May, 1959.

13. Leppert, G. and Nimmo, B. G., "Laminar Film Condensation on
Surfaces Normal to Body or Inertial Forces", Journal of Heat
Transfer, 90, pp. 178-179, February, 1968.

14. Gray, V. H., Marto, P. J. and Joslyn, A. W., "Boiling Heat
Transfer Coefficients, Interface Behavior, and Vapor Quality in
Rotating Boiler Operating to 475 G's", NASA- TN D-4136, March,
1968.

15. Marto, P. J. and Gray, V. H., "Effects of Acceleration on
Nucleate Boiling of Water in a Rotating Boiler", NASA Technical
Note (To be published).

I—

a:
uu

■z.

o
o

<
LU

CL.

a:
o
co

a:
o

I—
<t
a:
o
a.

CJ>

SATURATION PRESSURE, P,

1.7

2.9

4.7

(psia)
7.5

11.5

fAPOR SONIC
VELOCITY LIMIT

106

NUCLEATE BOILING CRITICAL
HEAT FLUX LIMIT

=>
fe

4->

VAPOR ENTRAPMENT
VELOCITY LIMIT

§ 105

I-
<

7.2

WATER
0 - 1 deg
2700 RPM
NO OUTSIDE
THERMAL RESISTANCE

10*

120"

140

160

180

200

220

SATURATION TEMPERATURE, Tg (deg F)

FIGURE 2 COMPARISON OF ROTATING HEAT PIPE LIMITATIONS

CJ>

Q
O

•a:
co

«=C

I—

>-
co

o
o
o

LlI

CD
t— •
U.

I
O

4->

z
en

yS h = <»

1 h = •» <"*

^ t- h = 500

^ /^

^ /

/ ^— — """"-""~" h = 500

WATER, T$ = 212 deg F

NUSSELT SOL N

SIMILARITY SOL'N [10]

i i i i

800 1600 2400
ROTATIONAL SPEED, (RPM)

3200

4000

FIGURE 4

COMPARISON OF NUSSELT FILM CONDENSATION SOLUTION
TO SPARROW AND HARTNETT [10] SIMILARITY SOLUTION
FOR HALF-CONE ANGLE, 0 * 1 DEGREE

h =

h = 500

WATER, T$ = 212 deg F

NUSSELT SOL'N

SIMILARITY SOL'N [10]

I I

800 1600 2400
ROTATIONAL SPEED, (RPM)

3200

4000

FIGURE 5

COMPARISON OF NUSSELT FILM CONDENSATION SOLUTION
TO SPARROW AND HARTNETT [10] SIMILARITY SOLUTION
FOR HALF-CONE ANGLE, d « 2 DEGREES

I
o

4-»

y h ~ •

/
/

Tr^"500""

^s^^ _

^ — "V T= 500

WATER, T$ = 212 deg F

~" NUbbtLI MJL N

SIMILARITY SOL'N [10]

till

800 1600 2400
ROTATIONAL SPEED, (RPM)

3200

4000

FIGURE 6

COMPARISON OF NUSSELT FILM CONDENSATION SOLUTION
TO SPARROW AND HARTNETT [10] SIMILARITY SOLUTION
FOR HALF-CONE ANGLE, 0=3 DEGREES

o
o

«=C

CJ»

UJ
Q

l/>

UJ
Q

Lu
O

Oi
O

<c
a:

UJ
CD

I
O

2 9

h =

h = 500

WATER

Ts = 212 deg F

800 1600 2400
ROTATIONAL SPEED, (RPM)

3200

4000

FIGURE 8

IMPROVED NUSSELT FILM CONDENSATION SOLUTION
FOR ROTATING CYLINDER, (3 = 0 DEGREES

Q.
<

LJ
I
CJ
CO

LlI
CC

Ld
CL

LU
CO

CO
CO

o
cc
o

LxJ

CO
CO

an
o

•— t

Q.
CO

CD
O

H-

CD
►— l

a:
o

CD
O

I—
O

CNJ

=3
CD

=>
_i

o.
o

LU
CO

LU
O

re
a.

rr»

DISTRIBUTION LIST

1 . B. T. Lundin
Director, LRC*, MS 3-2

2. E. J. Manganiello

Deputy Director, LRC*, MS 3-2

3. J. F. Connors

Asst. to Director, LRC*, MS 3-15

4. P. E. Foster

Technology Utilization Office, LRC*, MS 3-19

5. N. T. Musial

Patent Counsel, LRC*, MS 500-311

6. J. B. Esgar

Asst. Chief, Airbreathing Engines Division,
LRC*, MS 60-4

7. N. D. Sanders

Chief, Special Projects Division,
LRC*, MS 100-1

8. U. H. von Glahn

Head, Applied Research Branch,
Special Projects Division
LRC*, MS 11-1

9. V. H. Gray

Head, Experiments Section,
Special Products Division,
LRC*, MS 11-1 (5 copies)

10. J. C. Evvard

Associate Director, Advanced Research Institute
LRC*, MS 3-5

♦Lewis Research Center, 21000 Brookpark Road, Cleveland, Ohio 44135

11. R. Siegel

Head, Analytical Section, Physics and Chemistry Division
LRC*, MS 501-4

12. R. W. Graham

Head, Experimental Section, Physics and Chemistry Division
LRC*, MS 501-4

13. B. Lubarsky

Asst. Director for Power
LRC*, MS 3-3

14. R. E. English

Chief, Space Power Systems Division
LRC*, MS 500-201

15. J. A. Heller

Head, Rotating Components Section,
Space Power Systems Division
LRC*, MS 500-201

16. E. E. Bisson

Associate Chief, Fluid System Components Division
LRC*, MS 5-3

17. D. A. Petrash

Head, Space Environment Branch, Spacecraft Technology Division
LRC*, MS 54-1

18. M. Gutstein
LRC*, MS 500-201

19. J. Sweeney
LRC*, MS 500-302

20. W. 0. Logan, Jr.
LRC*, MS 3-13

21. J. W. Miser
LRC*, MS 3-13

♦Lewis Research Center, 21000 Brookpark Road, Cleveland, Ohio 44135

22. H. S. Snyder

Code: DHC, HDQTRS**

23. J. J. McDonald

Negotiator, Code: DHC-5, HDQTRS**

24. A. J. Evans

Director of Aeronautical Vehicles Division
Code: RA, HDQTRS**

25. A. 0. Tischler

Director, Chemical Propulsion Division
Code: RP, HDQTRS**

26. W. H. Woodward

Director, Space Power and Electric Propulsion Division
Code: RN, HDQTRS**

27. S. V. Manson

Chief of Nuclear Power Systems
Code: RNP, HDQTRS**

28. T. T. Neill

Chief of Technical Publications Branch
Code: RMP, HDQTRS**

29. Dr. H. H. Kurzweg

Director of Research Division
Code: RR, HDQTRS**

30. M. B. Ames, Jr.

Director Space Vehicle Division
Code: RV, HDQTRS**

31. S. Katzoff

Langley Research Center

MS 116

Hampton, Virginia

NASA Headquarters, Washington, D.C. 20546

32. Dr. S. C. Garg

Senior Project Engineer

Naval Civil Engineering Laboratory

Port Hueneme, California 93047

33. J. P. Kirkpatrick

NASA, Ames Research Center
Moffett Field, California

34. J. C. Chato

Assoc. Professor of Mechanical Engineering
University of Illinois
Urbana, Illinois

35. C. A. Busse
Euratom

Joint Nuclear Research Center
Ispra (Varese), Italy

36. H. W. Hoffman

Oak Ridge National Laboratory

P.O. Box X

Oak Ridge, Tennessee

37. Dr. B. D. Marcus
Manager, Heat Pipe Projects
TRW Systems Group
Redondo Beach, California

38. Dr. K. T. Yang

Chairman, Dept. of Mechanical and Aero-Space Engineering
University of Notre Dame
Notre Dame, Indiana

39. LTJG T. J. Daley, USN
Nuclear Power School
Naval Training Command
Bainbridge, Maryland

40. LT L. J. Ballback, USN
722 Delaware Avenue
Norfolk, Virginia 23513

41. Defense Documentation Center (DDC)
Cameron Station

Alexandria, Virginia 22314 (20 Copies)

42. Naval Postgraduate School
Code 02

Code 023 (2 Copies'
Code 0212 (2 Copies
Code 59Mx (20 Copies)
Code 59 (2 Copies)

UNCLASSIFIED

Security Classification

DOCUMENT CONTROL DATA -R&D

(Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified)

I originating activity (Corporate author)

Naval Postgraduate School
Monterey, California 93940

2». REPORT SECURITY CLASSIFICATION

Unclassified

26. GROUP

3 REPORT TITLE

An Analytical and Experimental Investigation of Rotating, Non-Capillary
Heat Pipes

4 descriptive NOTES (Type of report and.inclusive dates)

Annual Report, September, 1969 - June 1970

S au THOR(S) (First name, middle initial, last name)

Paul J. Marto
Leonard J. Ball back
Thomas J. Daley

6. REPORT DATE

30 June 1970

7«. TOTAL NO. OF PASES

76. NO. OF REFS

8a CONTRACT OR GRANT NO.

6. PROJEC T NO

9a. ORIGINATOR'S REPORT NUMBER(S)

NPS - 59MX70061A

c. NASA , Defense Purchase
Request W-l 3,007

96. OTHER REPORT NOISI (Any other numbers that may be assigned
this report)

10 DISTRIBUTION STATEMENT

This document has been approved for public release and sale; its distribution
is unlimited.

II. SUPPLEMENTARY NOTES

12. SPONSORING MILI TARY ACTIVITY

13. ABSTRAC T

The design and manufacture of an experimental rotating heat
pipe apparatus is also described.

""" 1473

I NOV 68 I "T I W

S/N 0101 -807-681 1

(PAGE 1)

UNCLASSIFIED

Security Classification

A- a 1408

UNCLASSIFIED

Security Classification

key wo RDS

ROLE W T

Heat Pipe, rotating
Heat Pipe, wickless
Film Condensation

DD ,F°1M..1473 back,

S/N 0101 -807-682!

UNCLASSIFIED

Security Classification

A- 31 409

U133987

DUDLEY KNOX LIBRARY - RESEARCH REPORTS

5 6853 01068949 0

Internet Archive Audio

Featured

Top

Images

Featured

Top

Software

Featured

Top

Books

Featured

Top

Video

Featured

Top

Mobile Apps

Browser Extensions

Archive-It Subscription

Save Page Now

Full text of "An analytical and experimental investigation of rotating, non-capillary heat pipes : annual report"

See other formats